The survival of nonattractive interacting particle systems on Z
Sudbury, Aidan
Ann. Probab., Tome 28 (2000) no. 1, p. 1149-1161 / Harvested from Project Euclid
We consider interacting particle systems on $Z$ which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b,c, d, e . We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from any finite occupied set. In particular: an IPS with rates a b c d e has a positive probability of survival if $$ b > 4d + 6a, \quad c + a \geq d + e$$ or $$ b > 7d + 3a - 3c + 3e, \quad c + a < d + e.$$ ¶ We create a suitable supermartingale by extending the method used by Holley and Liggett in their treatment of the contact process.
Publié le : 2000-06-14
Classification:  Interacting particle systems,  contact process,  critical values,  submartingale,  60K35
@article{1019160329,
     author = {Sudbury, Aidan},
     title = {The survival of nonattractive interacting particle systems on
		 Z},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 1149-1161},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160329}
}
Sudbury, Aidan. The survival of nonattractive interacting particle systems on
		 Z. Ann. Probab., Tome 28 (2000) no. 1, pp.  1149-1161. http://gdmltest.u-ga.fr/item/1019160329/